Determine the angle θ between the two cords

 Determine the angle θ between the two cords

Answer ;- 

From the figure :-

The coordinate of point A is (0,0,0,)

The coordinate of point B is (0,-3,4,)

The coordinate of point C is (2,3,6,)

 

So, The vector  AB is 

AB = B - A = -3j + 4k

And , magnitude of AB is 

| AB |  = 5 

 

 

 

Also , the vector BC is 

BC = B - C = 2i + 3j + 6k

And , magnitude of AB is 

| BC |  = 7

So, We know that By the dot product

Cosθ =  AB.BC/ |BC| . |AB|

Cosθ = (-3j+4k).(2i+3j+6k)/(5).(7) 

So,  θ = 64.23 Degree

Hence , the angle between the cords AN and BC is 64.23 degree.